Keeping your money safe is important! Sure you could store everything on Coinbase or Binance in the accounts there. But honestly, the whole point of cryptocurrencies is to “be your own bank”.
What I use, and also recommend at the moment is the Ledger Nano S (link).
This is an amazing device to keep everything safe. They have great support and are continually adding more coins to it.
If you are invested into non-supported coins you also have the option of combining your Ledger with MEW (my ether wallet). This gives you the option to store coins on your Ledger without the official coin app from Ledger.
The Ledger Nano S is an amazing device to keep your money safe. But I’m also looking forward to the Ethos Universal wallet which you can read more about here.